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Introduction to AntiRings

Author: A.A.A. Agboola

Publisher: Infinite Study

Published: 2020-10-01

Total Pages: 16

ISBN-13:

The objective of this paper is to introduce the concept of AntiRings. Several examples of AntiRings are presented. Specifically, certain types of AntiRings and their substructures are studied. It is shown that nonempty subsets of an AntiRing can be AntiRings with algebraic properties different from the algebraic properties of the parent AntiRing under the same binary operations. AntiIdeals, AntiQuotientRings and AntiRingHomomorphisms are studied with several examples. It is shown that the quotient of an AntiRing factored by an AntiIdeal can exhibit algebraic properties different from the algebraic properties of the AntiRing.

Introduction to NeutroHyperGroups

Author: M. A. Ibrahim

Publisher: Infinite Study

Published: 2020-12-01

Total Pages: 18

ISBN-13:

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NeutroSophication and AntiSophication are processes through which NeutroAlgebraic and AntiAlgebraic structures can be generated from any classical structures. Given any classical structure with m operations (laws and axioms) we can generate NeutroStructures and AntiStructures. In this paper, we introduce for the first time the concept of NeutroHyperGroups.

Neutrosophic Sets and Systems. An International Journal in Information Science and Engineering, Vol. 36, 2020

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2020-10-01

Total Pages: 410

ISBN-13:

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Neutrosophic Sets and Systems (NSS) is an academic journal, published quarterly online and on paper, that has been created for publications of advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics etc. and their applications in any field.

Neutrosophic Sets and Systems, Vol. 36, 2020

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 410

ISBN-13:

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“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles in this issue: n-Refined Neutrosophic Modules, A Neutrosophic Approach to Digital Images, A Novel Method for Neutrosophic Assignment Problem by using Interval-Valued Trapezoidal Neutrosophic Number.

Neutrosophic Sets and Systems, Vol. 38, 2020

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 662

ISBN-13:

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NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World

Author: Smarandache, Florentin

Publisher: IGI Global

Published: 2023-05-15

Total Pages: 280

ISBN-13: 1668447428

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NeutroAlgebra and AntiAlgebra were extended to NeutroGeometry and AntiGeometry in order to catch the Non-Euclidean Geometries. In the real world, the spaces and the elements that populate them and the rules that apply to them are not perfect, uniform, homogeneous, or complete. They are fragmentary and disparate, with unclear and conflicting information, and they do not apply in the same degree to each element. Therefore, these partial, hybrid, and mixed structures are necessary. NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World presents applications of many NeutroStructures in our real world and considers NeutroGeometry and AntiGeometry as new fields of research that resemble everyday life. Covering key topics such as hyperbolic geometry, elliptic geometry, and AntiGeometry, this reference work is ideal for mathematicians, industry professionals, researchers, scholars, academicians, practitioners, instructors, and students.

Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras

Author: Smarandache, Florentin

Publisher: IGI Global

Published: 2022-04-15

Total Pages: 333

ISBN-13: 1668434970

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Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are well-defined, but this is a restrictive case because there are situations in science where a law of composition defined on a set may be only partially defined and partially undefined, which we call NeutroDefined, or totally undefined, which we call AntiDefined. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebra introduces NeutroAlgebra, an emerging field of research. This book provides a comprehensive collection of original work related to NeutroAlgebra and covers topics such as image retrieval, mathematical morphology, and NeutroAlgebraic structure. It is an essential resource for philosophers, mathematicians, researchers, educators and students of higher education, and academicians.

Relations: Concrete, Abstract, And Applied - An Introduction

Author: Herbert Toth

Publisher: World Scientific

Published: 2020-06-22

Total Pages: 573

ISBN-13: 9811220360

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The book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.This book is unique by the spectrum of the topics it handles. As indicated in its title these are:

Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited)

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 16

ISBN-13:

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In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined. Again, in all classical algebraic structures, the Axioms (Associativity, Commutativity, etc.) defined on a set are totally true, but it is again a restrictive case, because similarly there are numerous situations in science and in any domain of knowledge when an Axiom defined on a set may be only partially-true (and partially-false), that we call NeutroAxiom, or totally false that we call AntiAxiom. Therefore, we open for the first time in 2019 new fields of research called NeutroStructures and AntiStructures respectively.

Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited)

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 16

ISBN-13:

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